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Two characterizations of finite quasi-Hopf algebras

Peter Schauenburg
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Abstract

Let H be a finite-dimensional quasibialgebra. We show that H is a quasi-Hopf algebra if and only if the category of its finite-dimensional left modules is rigid if and only if a structure theorem for Hopf modules over H holds. We also show that a dual structure theorem for Hopf modules over a coquasibialgebra H holds if and only if the category of finite-dimensional right H-comodules is rigid; this is not equivalent to H being a coquasi-Hopf algebra.

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Peter Schauenburg. 2002-07-08. Two characterizations of finite quasi-Hopf algebras. https://arxiv.org/abs/math/0207069

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